Simplify the following expression: $x = \dfrac{15z + 25}{-30}$ You can assume $z \neq 0$.
Find the greatest common factor of the numerator and denominator. The numerator can be factored: $15z + 25 = (3\cdot5 \cdot z) + (5\cdot5)$ The denominator can be factored: $-30 = - (2\cdot3\cdot5)$ The greatest common factor of all the terms is $5$ Factoring out $5$ gives us: $x = \dfrac{(5)(3z + 5)}{(5)(-6)}$ Dividing both the numerator and denominator by $5$ gives: $x = \dfrac{3z + 5}{-6}$